Mr Carmichael was asked by the House of Lords' Constitution Committee whether Scottish MPs should be allowed to vote on English law during that interim period.

He replied: "That essentially will be a question to be resolved on the other side of the general election."

Mr Carmichael added: "How that would play out ultimately would be dependent on the views of the returned members after May 2015 and indeed the terms of the debate that had taken them there."

The possibility that Lords based in Scotland may also be able to keep their peerages was raised by Lord Wallace of Tankerness QC, the Advocate General for Scotland.

He said that if a Lord continued to pay tax in the UK they may be able to still attend the Lords after independence.

Lord Wallace said the issue would be "whether people thought it was worth paying income tax in two separate countries to continue their membership of the House of Lords".

The comments raise the possibility of Scots continuing to shape future UK legislation despite representing a country leaving the Union.

Conservative MPs from English constituencies reacted with fury on Wednesday, saying the position would be undemocratic and unconstitutional.

"If Scotland votes for independence then they have voted for independence - Scottish MPs would have to stop voting on matters to do with what would be the rest of the United Kingdom," said Peter Bone, a Tory MP for Wellingborough.

"It would be completely ridiculous having voted to come out for their MPs to have a say on another country's business."

Mr Bone said the situation would be an "extraordinary state of affairs" and called for Scottish MPs to agree before the referendum not to vote on English law if independence wins out.

Bill Cash, a Tory MP for Stone, called the situation "inconsistent and unconstitutional", saying: "It is just inappropriate for Scottish members to be voting on matters which don't effect them [but] which do effect us."

Adam Holloway, Tory MP for Gravesham, said: "Why should matters that effect my constituents be voted upon by Scottish MPs in areas that are already devolved? It is quite wrong."

A House of Lords spokesman confirmed that all members must be UK domiciled taxpayers.